The first mistake is they used a non-constant-time scalar multiply. So, first do that. Of course that just hides the timing, not the power usage. There is a

The first mistake is they used a non-constant-time scalar multiply. So, first do that. Of course that just hides the timing, not the power usage. There is a bunch of elliptic curve stuff you can do like "multiplicative blinding", e.g. https://www.iacr.org/archive/ches2010/62250433/62250433.pdf https://www.iacr.org/archive/ches2010/62250433/62250433.pdf.